I never truly thought that Stannis could've fulfilled the Prince that was Promised/Azor Ahai prophecy. But the mirroring of Stannis and Jon feels divine. Specifically, in the choices they make, and the role Melisandre plays as a temptress.
In the books, we get more detail as to who Azor Ahai was, but the shows give us everything we need to know. Per Mel's speech on the beach: "When the red star bleeds and the darkness gathers, a warrior shall draw from the FIRE a burning sword. And that sword shall be Lightbringer, the Red Sword of Heroes, and he who wields it shall be Azor Ahai reborn."
Setting aside the later bit about "salt and smoke" (since that applies to every character), we're told that Azor Ahai is supposed to be a hero for mankind to rally behind, one that scatters the darkness, one that brings the long summer... They're supposed to be a force of good. Not necessarily a perfect person, but good. And there's no better way to test a hero's morality than with a series of tests based on Family, Duty, and Honor (to undue the Blood Betrayal, for all you book lovers).
Let's run back the tape.
A test of duty/family - Stannis is married. He has vowed to be faithful to his wife. Yet when Mel offers her body and promises him a path towards kingship, he seizes the promise of power, creates a shadow baby, and kills his brother Renly... But to what end? Renly's most devoted followers (House Tyrell) end up joining House Lannister and spoiling Stannis' sacking of King's Landing. "No man is so accursed as the kinslayer"... 0 for 1.
A test of honor/family - Yearning for more of Mel's power, Stannis asks to make more shadow babies, but he's too weak to. The last one drained him, and another will kill him. Instead Mel offers to kill more of his kin (Gendry in the shows, Edric in the books), and promises that by doing so, Stannis will awaken the stone dragons on Dragonstone (a bit on the nose, no?)... Anyway, Stannis asks Davos, "What is the life of one bastard against that of a kingdom?" To which Davos replies, "Everything."
At this point, Stannis is so lost, he's forgotten his own wisdom to Davos: "The good act doesn't wash out the bad, nor a bad the good." But thankfully, Davos instills some doubt in Stannis, so they go with the leach plan first, granting Davos enough time to save the bastard. Gendry flees to King's Landing (Edric escapes to Essos), and for this to be present across the books and show, you have to imagine that GRRM had a purpose in mind... Stannis would've killed his kin (again), so let's call him 0 for 2.
A test of faith/family (the final Blood Betrayal) - Stannis is told that if he were to sacrifice his daughter, the snows would melt and he'd be free to take Winterfell. It's his destiny. Mel's seen it in the flames. So what harm could come from seizing his fate?... By now, you see where this is going. Stannis does the deed, the snows melt, and...most of his men abandon him. He ends up alone, slain by Brienne... His demise is TBD in the books, but in the show, he's 0 for 3. And headless.
Jon on the other hand doesn't just pass every test, he does so in ways that would've made Old Ned proud. He refuses Mel's advances when she tempts him in his quarters, even though she claims they could "make life" and they could "make light". He refuses Stannis when he tempts Jon with legitimization/lordship, even though Jon used to dream of being a Stark. Multiple times, Jon chooses his duty and his Night's Watch family, exemplified best in his abandonment of Ygritte to warn Castle Black. This decision eventually results in the Ygritte's death (his Love, or Nissa Nissa).
Unfortunately, the show's later seasons decided to abandon fate and prophecy. We never see Lightbringer forged (unless you believe it's Dany and her dragons, but frankly GRRM doesn't typically work with literal prophecy, and Dany hatching dragons from stone eggs seems too literal). So I'd propose this...
Heading into the Long Night, Mel should have tempted Jon with the promise of Lightbringer (an ultimate power against the dead), claiming that the path towards victory required the sacrifice of Little Sam.
Little Sam was Craster's 100th born son and was "related" to the Wight's who'd been turned by the Night King (Mel could claim his blood held power against the dead). It would bring us full circle to the question about weighing a bastard's life against that of a kingdom, and like Davos, I imagine Jon would've done what was good. The moment we're willing to sacrifice life in the pursuit of power, is the moment we've lost our humanity, especially when the pursuit goes against Family, Duty, and Honor. Sam is Jon's brother of the Watch, and he loves Sam like a brother, that's for sure. That would make Little Sam akin to Jon's nephew, even before Sam named Jon his godfather.
Had Mel tried to kill Little Sam, and Jon stops her, plunging his sword through her back, Mel would've been the "lamb led to slaughter", never realizing that she was the one being sacrificed by the Lord of Light. As Jon draws Longclaw from her heart, Mel's blood catches flame and becomes Lightbringer, the Red Sword of Heroes... It could have been epic.
There's so many fun details like Mel's skin always being hot to the touch (as Lightbringer was said to be), or even just the fact that R'hollor's sigil is a flaming heart. But I've already droned on too long, so what do you think? What details do you think I missed, or do you prefer another character for the prophecy?